Research-Colloquium

Geometric Langlands and co-adjoint orbits

Abstract

Geometric Langlands can be interpreted as a mirror symmetry between the moduli space of Higgs bundle of group $G$ via the same moduli space of its Langlands dual $G'$. Once we consider the insertion as a form of parabolic structure or more generally coadjoint orbit, it is clear that the conjectural mirror symmetry of moduli space of Higgs bundle requires a version of mirror symmetry between coadjoint orbits. In the talk, we will explore the possible "coadjoint orbit mirror symmetry".

About the speaker

Yongbin Ruan is currently a professor at the Institute for Advanced Study (IAS) of Zhejiang University. He was elected to the Chinese Academy of Sciences in 2021 and an invited speaker of the 1998 ICM. Professor Ruan works in the field of symplectic geometry and mathematical physics. He is credited with a few well-known theories, such as the (orbifold) Gromov-Witten theory, relative Gromov-Witten theory, Chen-Ruan cohomology, and Fan-Jarvis-Ruan-Witten theory, and for the resolution of several outstanding conjectures, such as the Arnold conjecture, the generalized Witten conjecture, and the LG/CY correspondence conjecture.